Superconductivity in inhomogeneous Hubbard models

We present a controlled perturbative approach to the low-temperature phase diagram of highly inhomogeneous Hubbard models in the limit of small coupling, t('), between clusters. We apply this to the dimerized and checkerboard models. The dimerized model is found to behave like a doped semiconductor, with a Fermi-liquid groundstate with parameters (e.g., the effective mass) which are smooth functions of the Hubbard interaction, U. By contrast, the checkerboard model has a Fermi liquid phase at large U>U-c=4.58, a d-wave superconducting state with a full gap for U-c>U>0, and a narrow strip of an intermediate d-wave superconducting phase with gapless nodal quasiparticles for parallel to U-U-c parallel to < O(t(')).